04/09/2015
Gunnery Control and Norbert Wiener
"The world, understood cybernetically, was a world of goal-oriented feedback mechanisms with learning. Cybernetics,then, took computer-controlled gun control and layered it in an ontologically indiscriminate fashion across the academic disciplinary board."
Gunnery Control and Jay Forrester
Less than fully rational agents are hard
Start from the opposite direction
Use simple trial and error
Feedback vs Feedforward
Here
Zero-Intelligence (Plus)
Probe and Adjust
Gjerstad and Dickhaut
A seller wants to sell \(y^*\) units of a good each day. Today he charged price \(p_t\) and sold \(y_t\) units. How should he sets tomorrow's price \(p_{t+1}\)
\(e_t = y^* -y_t\)
\(p_{t+1} = a e_t + b \sum_0^t e_{\tau} d\tau + c \frac{de_t}{d_t}\)
Trial and Error
Modular
Can be extended to buying
Multiple independent control problems
Need to set production rates that maximize profits
Lower frequency
How to choose production?
Hill-Climbing
Marginal Maximizer
Profits are maximized when marginal benefits equal marginal costs
\(p_t + \mu_p = w_t + \mu_w\)
Use a PID with error \(p_t + \mu_p - w_t + \mu_w\)
PI trial and error produce paired data \(p_t,y_t\)
Can run a linear regression over them to discover \(\mu_p\)
Use Kalman Filters
Sticky prices and price rigidities
Why are prices sticky?
A model where sticky prices are superior to flexible ones
PID seller changes price to elicit a response in the quantity demanded
Maximization happens at a lower frequency than price changes
Downstream zero knowledge firms adapt labor slowly to upstream price changes
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